References

FHI-aims is an all-electron electronic structure code that uses localized, numerically tabulated atom-centered basis functions to discretize the orbitals and wave functions of electronic structure theory. This choice enables a high-precision representation of the orbitals and density of complex nano-structures with reasonable computational effort across the periodic table, including all core and valence electrons (no shape approximations to potentials or wave functions).

• The extension of NEO-DFT from molecular only case to periodic systems:

  J. Xu, et al., "Nuclear–electronic orbital approach to quantization of protons in periodic electronic structure calculations", J. Chem. Phys. 156, 224111 (2022). https://doi.org/10.1063/5.0088427

• RT-NEO-TDDFT for periodic systems:

  J. Xu, et al., "First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems", Phys. Rev. Lett. 131, 238002 (2023) https://doi.org/10.1103/PhysRevLett.131.238002

• Systemetic derivation of RT-NEO-TDDFT, NEO Ehrenfest dynamics, and energy gradients:

  J. Xu, et al., "Lagrangian Formulation of Nuclear-Electronic Orbital Ehrenfest Dynamics with Real-time TDDFT for Extended Periodic Systems". https://doi.org/10.48550/arXiv.2407.18842

• The construction of basis sets for density-functional theory and the elementary numerical choices:

  V. Blum, et al., "Ab initio molecular simulations with numeric atom-centered orbitals", Comput. Phys. Commun. 180, 11 (2009). https://doi.org/10.1016/j.cpc.2009.06.022

• The electron proton correlation functionals:

  Y. Yang, et al., "Development of a practical multicomponent density functional for electron-proton correlation to produce accurate proton densities", J. Chem. Phys. 147, 114113 (2017). https://doi.org/10.1063/1.4996038

• The optimized proton basis sets with gaussian:

  Q. Yu, et al., "Development of nuclear basis sets for multicomponent quantum chemistry methods", J. Chem. Phys. 152, 244123 (2020). https://doi.org/10.1063/5.0009233